A constitutive model for fault gouge deformation in dynamic rupture simulations

Abstract

[1] In the context of numerical simulations of elastodynamic ruptures, we compare friction laws, including the linear slip-weakening (SW) law, the Dieterich-Ruina (DR) law, and the free volume (FV) law. The FV law is based on microscopic physics, incorporating shear transformation zone (STZ) theory which describes local, nonaffine rearrangements within the granular fault gouge. A dynamic state variable models dilation and compaction of the gouge, and accounts for weakening and restrengthening in the FV law. The principal difference between the FV law and the DR law is associated with the characteristic length scale L. In the FV law, L FV grows with increasing slip rate, while in the DR law L DR is independent of slip rate. The length scale for friction is observed to vary with slip velocity in laboratory experiments with simulated fault gouge, suggesting that the FV law captures an essential feature of gouge-filled faults. In simulations of spontaneous elastodynamic rupture, for equal energy dissipation the FV law produces ruptures with smaller nucleation lengths, lower peak slip velocities, and increased slip required for friction to fully weaken to steady sliding when compared to ruptures governed by the SW or DR laws. We also examine generalizations of the DR and FV laws that incorporate rapid velocity weakening. The rapid weakening laws produce self-healing slip pulse ruptures for low initial shear loads. For parameters which produce identical net slip in the pulses of each rapid weakening friction law, the FV law exhibits a much shorter nucleation length, a larger slip-weakening distance, and less frictional energy dissipation than corresponding ruptures obtained using the DR law.

Seismicity in a model governed by competing frictional weakening and healing mechanisms

“…According to the underlying Shear Transformation Zone (STZ) theory (Falk & Langer 1998, microscopic configurational rearrangements within the gouge occur much more slowly than macroscopic stress equilibration, suggesting a mechanism for the continued change of a gouge state over long time scales . Applying the theory within an elastodynamic framework, Daub & Carlson (2008) showed that small differences in shear strain localization influences the nucleation, propagation, and arrest of elastodynamic ruptures and can thus lead to drastically different results for earthquake simulations.…”

“…The properties of gouge layers govern the evolution of the frictional resistance during dynamic instabilities and therefore the behaviour of earthquake faults (e.g. Scholz 1990; Chambon et al 2006;Daub & Carlson 2008). The response of structurally simpler, relatively smooth faults with consolidated wear products is typically characterized by slip or velocity weakening, associated with smaller G values.…”

The seismic cycle at subduction thrusts: 2. Dynamic implications of geodynamic simulations validated with laboratory models

“…To our knowledge, numerical geodynamic models studying seismicity [e.g., Huc et al, 1998;Cattin and Avouac, 2000;Fuller et al, 2006;Chery and Vernant, 2006;Lecomte et al, 2012] do not include an evolving rate-dependent friction coefficient (or strain rate weakening) to simulate frictional instabilities. A ratedependent friction has, however, been included in continuum models with stick-slip instabilities in shear bands following the Shear-Transformation-Zone (STZ) model [e.g., Daub and Carlson, 2008;Daub and Carlson, 2009]. Their model describes plastic deformation based on grain-scale physics in amorphous materials and fault gauges [Falk and Langer, 1998].…”

Effective temperature dynamics of shear bands in metallic glasses

“…Our identification of relaxation as a mechanism for producing rate-weakening behavior, while the dissipation term produces rate-strengthening behavior, resolves previous disagreements between STZ theory and velocity step experiments [13] that showed both rate-weakening and rate-strengthening behavior at different temperatures. Previous version of STZ theory have shown that the model is either rate strengthening or rate weakening [31,54,63], and simulations tend to show rate-strengthening behavior [56,57]. Further, the behavior of the dissipation and relaxation terms over different temperature and strain-rate regimes goes beyond explaining the rate dependence and simultaneously matches the stress overshoot and steady-state stress observations in a quantitative fashion.…”

“…Some approaches start from an inherently liquidlike model [20,21], to which solidlike features are added, while others are based on a solidlike starting point and incorporate liquidlike flow through flow defect mechanisms [22][23][24]. One example of a solidlike flow defect model is shear transformation zone (STZ) theory [16,25], which has been applied to a wide range of amorphous materials, including metallic glasses [26][27][28], granular materials [29], and earthquake faults [30][31][32][33]. While STZ theory has been successful in many situations, several of its ingredients remain poorly constrained by data, and further work is needed to assess the validity of many of its assumptions.…”